Superconvergent HDG methods for linear elasticity with weakly symmetric stresses

Bernardo Cockburn, Ke Shi

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

We provide a systematic way of devising superconvergent mixed and hybridizable discontinuous Galerkin (HDG)methods for linear elasticity based on weak stress symmetry formulations. We show that, by suitably modifying the spaces defining superconvergent mixed and HDG methods for diffusion obtained in Cockburn et al. (Conditions for superconvergence of HDG methods for second-order elliptic problems, Math. Comp., 81, 1327-1353.), we obtain optimally convergent approximations for all unknowns, as well as a superconvergent approximation of the displacement. We use a projection-based a priori error analysis to achieve this goal.

Original languageEnglish (US)
Pages (from-to)747-770
Number of pages24
JournalIMA Journal of Numerical Analysis
Volume33
Issue number3
DOIs
StatePublished - Jul 2013

Bibliographical note

Funding Information:
Supported in part by the National Science Foundation (Grant DMS-0712955) and by the University of Minnesota Supercomputing Institute.

Keywords

  • discontinuous Galerkin
  • hybridizable
  • linear elasticity
  • superconvergence

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